An Expert System Approach to Short-Term Load
Forecasting For Reliance Energy Limited, Mumbai
M. S. S. Rao, S. A. Soman, B. L. Menezes, Pradeep Chawande, P. Dipti, and T. Ghanshyam
Abstract— Economically efficient generation scheduling requires accurate forecasting of load. In this paper, we propose
a Short Term Load Forecasting program for Reliance Energy
Limited (REL) in Mumbai region. The method is based on a
similar day approach. The development of forecast engine involves
4-steps. The first step involves discussion with domain experts
(Utility Engineers) to extract and learn the rules regarding system
behaviour. In the next step, these rules are refined by statistical
analysis. A linear prediction model for each day of week is
developed. The third step involves an adaptive implementation of
the rules. The parameters of the linear model are learned from
previous data by solving an optimization problem. Quadratic
Programming is used with redundancy factor 2. The final step
involves fine-tuning of forecast by re-shaping the forecast as
the reference day using Fast Fourier Transform, filtering and
smoothening by 3-point moving average technique. Normalization
is done using dc component of reference day.
Since the parameters are learnt from past few weeks data, the
seasonal variations due to change in season like winter, summer
are better modeled. Detailed study of the results of the forecast
program, the overall Mean Absolute Percentage Error (MAPE)
of the forecasted data is 2.89 over an interval from Aug’04 to
May’05 which is reasonable.
Index Terms— Expert System Approach, Quadratic Programming, Short-Term Load Forecasting.
T
I. I NTRODUCTION
HE main aim of a power system is to produce electric
power as to satisfy consumer’s requirements at all times
and at reasonable cost. Short Term Load Forecasting (STLF)
plays an important role in electric power system operation and
planning. It is fundamental to provide economic generation,
system security, load management and planning. Forecast of
the total load demand is necessary for Unit Commitment
and Economic Dispatch of generating units. Short-term load
forecasting is also essential for system security and load
management. Western Region Electricity Board (WREB) has
implemented the Availability Based Tariff (ABT) [1]. Under
this tariff structure, the utilities are penalized for the unscheduled interchange i.e. for the over drawl and under drawl and
M. S. S. Rao is Ph D student at Indian Institute of Technology Bombay,
Mumbai (email:[email protected])
S A Soman is with Department of Electrical Engineering, Indian Institute
of Technology - Bombay, (e-mail: [email protected]), Phone No: 91-2225767435, Fax:91-22-25723707
B. L. Menezes is an Associate Professor in KReSIT, Indian Institute of
Technology - Bombay, (e-mail:[email protected])
Pradeep Chawande is a Senior Manager, Reliance Energy Limited,
Mumbai, (e-mail: [email protected])
P. Dipti (e-mail: [email protected]) and T. Ghanshyam (e-mail:
[email protected]), are Senior Engineers, Reliance Energy Limited, Mumbai
is frequency dependent. Accurate forecasting not only reduces
the generation cost in a power system, but also provides a good
principle of effective operation and increase the profits of the
electricity markets in the context of ABT.
This paper proposes a rule-based expert system for STLF
on Reliance Energy Limited Mumbai network.
This paper is organized as follows. In section II, the
parameters which affects the system load is discussed. Section
III deals with the data analysis. Section IV discuss the expert
system method for STLF and the rules for expert system.
Section V gives the results and Section VI concludes the paper.
II. T HE SYSTEM LOAD
The system load is the sum of all the individual demands
at all the nodes of the power system. In principle, one
could determine the system load pattern if each individual
consumption pattern were known. However, the demand or
usage pattern of an individual load of a customer is quite
random and highly unpredictable. Also, there is a very broad
diversity of individual usage patterns in a typical utility. These
factors make it impossible to predict the system demand
levels by extrapolating the estimated individual usage patterns.
Fortunately, however the totality of the individual loads results
in a distinct consumption pattern which can be statistically
predicted.
The system load behavior is influenced by a number of
factors [2]. These factors can be classified into four major
categories.
Economic factors
Time factors
Weather factors
Random disturbances.
To model the system load, one needs to understand the impact
of each class of factors on the electricity consumption patterns.
A. Economic Factors
The economic environment in which the utility operates has
a clear effect on the electric demand consumption patterns.
Factors, such as the service area demographics, levels of
industrial activity, changes in the farming sector, the nature
and level of penetration of the appliances in the population,
developments in the regulatory climate and more generally,
economic trends have significant impacts on the system load
growth/decline trend. In addition, utility-initiated programs,
such as changes in rate design and demand management
programs, also influence the load. Typically, these economic
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factors operate with considerably longer time constants than
one week. It is important to account for these factors in the
updation of forecasting modes from one year to the next or
possible from one season to another. The economic factors
are not, however, explicitly represented in the short term
load forecasting models because of the longer time scales
associated with them.
B. Time Factors
The main time factors that plays an important role in
influencing the load pattern are seasonal effects, weekly-daily
cycle, and public and religious holidays. The seasonal changes
determine whether a utility is summer or winter peaking.
Certain changes in the load pattern occur gradually in response
to seasonal variation such as the number of daylight hours
and the changes in temperature. On the other hand, there are
seasonal events which brings abrupt, but important structural
modifications in the electricity consumption pattern. These
are the shifts to and from Day-light Time, changes in the
rate structure(time-of-day or seasonal demand), start of school
year, and significant reductions of activities during vacation
periods.
The weekly- daily periodicity of the load is a consequence
of the work-rest pattern of the service area population. There
are well-defined load patterns for “typical” seasonal weeks.
The existence of statutory and religious holidays has the
general effect of significantly lowering the load values to
levels well below “normal”. Moreover, on days preceding
or following holidays, modifications in the electricity usage
pattern are observed due to the tendency of creating “long
weekends.”
C. Weather Factors
Meteorological conditions are responsible for significant
variation in the load patterns. This is true because most utilities
have large components of weather-sensitive load, such as
those due to space heating, air conditioning, and agriculture
irrigation.
In many systems, temperature is the most important weather
variable in terms of its effects on the load. For any given
day, the deviation of the temperature variable from a normal
value may cause significant changes as to require major
modifications in the unit commitment pattern. Moreover, past
temperatures also affects the load profile. For example, a string
of high-temperature days may result in such heat buildup
throughout the system as to create a new system peak. For a
system with nonuniform geography and climate, several temperature or several areas may need to be considered to account
for variations in the system load. Humidity is a factor that may
affect the system load in a manner similar to temperature,
particularly in hot and humid areas. Thunderstorms also have
a strong effect on the load due to the change in temperature
that they induce. Other factors that impact on load behavior
are wind speed, precipitation, and cloud cover/light intensity.
D. Random Disturbances
The power system is continuously subject to random disturbance reflecting the fact that the system load is a composite
of a large number of individual demands. In addition to a
large number of very small disturbances, there are large loadssteel mills, synchrotron, wind tunnels- whose operation can
cause large variations in electricity usage. Since the hours of
operations of these large devices are usually unknown to utility
dispatchers, they represent large unpredictable disturbances.
There are also certain events such as widespread strikes, shutdown of industrial facilities and special television programs
whose occurrence is known priori, but whose effect on the
load is uncertain.
III. DATA A NALYSIS
The data analysis is carried out on data provided by Reliance
Energy Limited (REL) in the Mumbai region. The REL is one
of the major distribution companies in Mumbai having peak
load of 1200MW and having its own generation of 500MW.
Forecast for the next day implies forecast from 00:00 hrs to
23:45 hrs of the next day. Forecast has to be given at 15:00 hrs
(previous day). Usually, accuracy of forecast improves as the
gap between time of forecast and forecast hours is reduced. In
the analysis phase, the load curves are drawn and the variation
of the load with temperature is studied.
A. Load Curves
The load data contains half hourly load data and minimum
and maximum temperature values of the day. The load curve
for the month of July-2004 is shown in Fig. 1. The observations from the load curves are as follows:
1) The shape of the load curve is almost the identical on
same week days, if the day is not a holiday.
2) The load shape is affected by holidays.
3) Average demand is almost same on the same week days.
4) The Fig. 1 clearly shows the weekly seasonality.
5) The Fig. 2 reveals that the shape of the load curve is
almost same on the same week day, but it scales up and
down.
6) Days are classified based on their load into the following
categories.
a) Normal
working day
Saturday
b) c) Holiday during the week
d) Holiday preceded or followed by weekend
e) Special days
f) Outliers
B. Variation of the load with Temperature
Temperature is the most important weather variable in terms
of its effects on the load. For any given day, the deviation of
the temperature variable from a normal value may cause significant load changes. Fig. 3 and 4 show the relation between
load and temperature. The graph shows the positive correlation
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Fig. 1.
Load curve for the month of July 2004.
Fig. 4.
A plot between the average load and average temperature.
TABLE I
Sun
Mon
Tue
Wed
Thu
Fri
Sat
B EST CORRELATED PREVIOUS DAY
best
best
best
Pre Sun
2 weeks back
3 weeks back
Sunday
Sunday
Thu
Fri
Mon
Thu
Mon
Tue
Tue
Thu
Mon
Tue
Wed
Thu
Thu
Wed
Tue
Thu
Wed
Tue
C. Correlation Analysis
Fig. 2.
Load curves of all Wednesdays in the months May to August 2004.
between load and temperature i.e. demand increases with
temperature. Fig. 3 is the plot between average temperature
and maximum demand. Fig. 4 is the plot between average load
and average temperature. Average temperature here is simply
the mean of maximum and minimum temperature of the day.
In the plots dot represents the actual values and the solid line
is the best fit curve.
The above load curves show good correlation on week days.
The correlation coefficient is used to study the correlation of
load data between the two days. The correlation coefficient
between two days is calculated using the equation 1. Here
the correlation coefficient is studied between particular day
and the last seven days, the corresponding day two weeks and
three weeks back. The same information is studied over an
year data for the other week days also. The best correlated
days for a particular day were given in the Table I.
(
"!
"!
#$&%
!
)
*,+
%'
!
&%
%-,+.
0/ +
(1)
)
From this correlation analysis we can find the best correlated
days and we can select them as reference days.
D. Auto Correlation Analysis
Fig. 3.
A plot between the average load and maximum temperature.
Autocorrelation Function(ACF) is the term used to describe
the association or mutual dependence between values of the
same time series at different time periods. This can be com!
!
puted using the general equation,
2
$! 8 9 2
:
6 8 132 54 7
(2)
+
8 4
The Fig. 5 show the autocorrelation function at different
time
lags. In this figure we can see that ACF of 48 time lag
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is high. This means that
there is
a seasonality and a good
correlation between 1 and 48 point which are 24 hours
apart. In other words today’s load has good correlation with
yesterday’s load at the same time.
Here is a constant, is the forecasted mean
temperature of target day and is the reference
day’s mean temperature.
average temperature is given by
"!$#&% 9 + "!('*) The
. The parameter ‘ ’ is optimized
for every month. Typical value of ‘ ’ for Sunday is 30. The
forecast data in the formula form is given by
547698
+-, 103:
0:00 to 6:00
2 ;=
<>? From
/.
From 06:15 to 23:45
:; is the reference day load.
Where
(4)
B. Monday model
Fig. 5.
Autocorrelation of load data at different time lags.
IV. A N E XPERT S YSTEM BASED M ETHOD FOR STLF
An expert system [3], [4] is one which can reason, explain
and have its knowledge. The expert systems represent the
expert knowledge as data or rules within the computer. These
rules and data can be called upon when needed to solve
problems. This rule based algorithm consists of the following:
Logical and syntactical relation between weather and
daily load shapes.
Set of relations between changes in the load and change
in the natural and forced factors.
Rule base consists of all rules taking the IF-THEN form
and mathematical expressions.
After a detailed study of data, we concluded that the load
data has correlation with the previous day load data on normal
week days (Tuesday to Friday) provided that the day is not
a holiday and there is not much variation in temperature on
that day. The load on Sundays is having high correlation with
previous Sundays. We use these conclusions to develop the
rule based algorithm.
A. Sunday model
The load curves and the correlation analysis shows that
Sunday is having good correlation with previous Sundays.
Thus the previous Sunday has been selected as reference day
(RD) if it is a normal day, else previous to previous, else
three weeks back Sunday is selected as reference day if it is a
normal day. Forecast for Sunday load from 0:00hrs to 6:00hrs
is the actual load of previous day, i.e the Saturday’s load. After
6:00hrs the forecast load is the reference day’s load times the
Temperature Correction Factor (TCF).
(3)
The best correlated days for Monday are previous Thursday,
Friday and Monday. The same order is used to select the
reference day for Monday if the target day and reference day
both are normal days. Forecast of the load from 0:00hrs to
03:00hrs is the actual load of previous day, i.e the Sunday’s
load. From 3:15hrs to 8:00hrs reference day is previous
). The
Tuesday multiplied by the load correction factor ( @
reason for choosing Tuesday is that the early Monday morning
load does not pick up in the same manner as early Sunday
morning load. After 08:00hrs the forecast load is the reference
day’s load times the Temperature Correction Factor (TCF).
47698
0:00 to 3:00
+-, ACB EF GI
D HKJJ L 747698 < @ From
From 03:15 to 08:00
:?;M<>?
From 08:15 to 23:45
(5)
=ratio of the average load on Sunday and Tuesday
Where @
represents the normalbetween 03:00 hrs to 08:00hrs. @
ization of one week back data with this week data.
C. Tuesday model
Since the load curves and the correlation analysis shows that
the Tuesday has good correlation with the previous Monday,
Tuesday, Thursday and Friday, a linear model can formed
using these days as in equation 6.
+-, 8
.
\[^]_
>< J 7476N8O Q< PSR L 476N8K T >< U J 4V698
+
W <>U J +NX(Y Z < 8
(6)
.
we
have some additional constraints like
W also
I`a"b
. If `a"b Sc , then the forecast load will
However
4
be the convex combination of good correlated days. However
in a generic frame work, the parameter `a"b can also be
optimized.This leads to a Linear Programming (LP) problem.
dZ
represents a temperature dependent offset parameter.
In the above problem the coefficients to Z can be
found using Quadratic Program (QP). Our aim is to learn
the best values of coefficients to Z using previous data.
The learning is adaptive and the coefficients are upgraded
each week based upon the last 10 weeks data. The MATLAB
inbuilt function “QuadProg” is used to solve for to Z and
substituted in the equation 6 for forecast on Tuesday. Most
recent 10 week data is used in the learning process. We would
like to claim that every half an hour interval leads to a different
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LP problem and hence, to Z are not average values on a
day.
Similarly, the models for Wednesday, Thursday, Friday and
Saturday have been developed and they summarized below.
D. Wednesday model
+-, 8 >< J 4V698 Q< PSR L 4V698 T < , 47698
+
W <>U J +NX(Y Z < 8 (7)
TABLE II
M EAN , M IN AND M AX MAPE S OVER THE PERIOD AUG ’04 TO M AY ’05.
Mean MAPE
Sun
Mon
Tue
Wed
Thu
Fri
Sat
All Data
2.9369
3.3787
2.8529
2.6366
2.6376
2.8558
2.9807
2.8944
Minimum
MAPE
0.88499
0.87954
0.95412
1.0543
0.65905
0.8773
0.6767
0.65905
Maximum
MAPE
9.5171
8.1652
7.4056
8.4326
6.9554
7.1751
10.244
10.244
E. Thursday model
+-, .
< , 47698 +
< J 476N8 T < V. R ESULTS
.
(8)
F. Friday model
+-, (6
<?
U J 476N8V
+
< , 476N87 T < $6
All the rules that are mentioned in section IV have been
coded in the MATLAB. The results are compared using Mean
Absolute Percent Error (MAPE), defined
as follows:
!
P
(9)
c
a R
J
)
,
+ R 1 V , R ,
V J R , 2
<
c
]]
(11)
G. Saturday model
+-, <U J 74 698V
+
<
1
476N87 T < A. MAPE Analysis
(10)
All the coefficients were found using QP and substituted
in equations 7 to 10 to get the forecast for Wednesday,
Thursday, Friday and Saturday respectively.
Remark 1. The above models are used upto 15:00 hrs when
the operator has to submit the load forecast for the next day.
Post 15:00 hr forecast can not use data after 15:00hrs of the
previous day as it is yet to happen. Hence, similar models
but with reduced information content are used for forecasting
after 15:00hrs.
The MAPE analysis shows that the mean, minimum and
maximum MAPEs on overall data are 2.8979, 0.659 and
10.24 respectively. Large MAPEs usually represents out-liers.
Handling the outliers requiring much more data and analysis,
which is beyond scope of this paper. Table II shows the values
of Mean MAPE, minimum MAPE, maximum MAPE for each
week day and overall data.
The pie chart in Fig. 6 shows that 81% of the days have
MAPE less than 4%, 8% of the times the MAPE is in between
4 and 5, and 11% of the times MAPE is greater than 5 which
is quite acceptable.
H. Holiday Forecasting
The data analysis reveals that the load on public holidays
(on week days) resembles that of Sunday. This is because that
the industries and offices are closed. Therefore, reference day
to forecast for holidays is taken as Sunday. The forecast data
for holiday is reference day times TCF.
I. Smoothening and Reshaping of the forecasted load curve
Since the forecast methods have different models for different time slots in a day, there may occur discrete jumps in the
forecast load, which is not desirable. To eliminate the changes
in the forecasted load, we have performed smoothing of raw
forecast. Smoothing is done in two steps.
1) Fast Fourier Transform (FFT) Smoothing.
2) 3-Point moving average smoothing.
By doing FFT of the forecasted load, we will get the frequency
domain data. By eliminating the higher harmonics which cause
the discrete jumps in the forecasted load, we can smooth
the variations in the forecast. Subsequently, a simple 3-point
moving average is used.
Fig. 6.
range.
Pie chart showing the percentage days having MAPE in the given
B. Study the Variation of coefficient
`a"b
As a part of reducing the error, the MAPEs are studied by
varying the `Vb . The Fig. 7 shows the MAPE as a function of
`a"b . The best fitted `Vb values are given in the Table III.
Reason for the variation of best `a"b :
1) The best fitted `a"b on Monday is 0.975 because Monday’s actual load is less than Thursday which is used for
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TABLE III
B EST FITTED Sun
1.00
Mon
0.975
Tue
1.01
Wed
1.00
1300
Thu
0.995
Fri
1.00
Sat
0.975
Load curves of the actual and forecasted on 15−Sep−05
1200
Load in MVA
1100
sensitivity of MAPE with beq
6.5
Sun
6
Mon
5.5
Tue
MAPE
Forecasted
Actual
900
800
Wed
5
1000
Thu
700
Fri
4.5
Sat
4
600
0
3.5
5
15
10
Time of the day
20
25
3
2.5
0.95
Fig. 7.
Fig. 8.
0.96
0.97
0.98
0.99
1
beq
1.01
1.02
1.03
1.04
MAPE Vs .
VII. ACKNOWLEDGMENT
the forecast of the Monday’s load. This implies that we
should not use different linear combination of models.
2) The best fitted `a"b on Tuesday is 1.01 because the
Tuesday’s load is greater than Monday’s load which is
used to forecast Tuesday’s load.
3) The best fitted `a"b for Saturday is 0.975 because Thursday’s load is greater than Saturday’s load.
C. Best values of coefficient of “ ”
was find out by
The best values of coefficient ‘ ’ in
trial and error. The best values of coefficient ‘ ’ for each day is
given in the Table IV. These values of ‘ ’ are usually updated
every month, so as to follows the gross changes in the system.
Fig. 8 shows the actual load curve and forecasted load curve
for 15-Sept-05. It is seen that forecast follows the actual load
pattern closely.
VI. C ONCLUSIONS
This paper proposed an expert system approach to STLF
applied to REL Mumbai, region. The basic idea is to use
similar day approach but the coefficients for linear model are
learnt by solving a quadratic programming problem over a
most recent few weeks data. This makes learning adaptive.
Results obtained over one year during Aug’04 to May’05 are
very encouraging. We feel that the proposed methodology is
generic enough to be applied to forecasting problem of other
distribution companies (DISCOM) / utilities.
TABLE IV
B EST FITTED Sun
30
Actual and forecasted load curve on 15-Sept-05.
1.05
Mon
22
Tue
36
Wed
34
The authors would like to thank Reliance Energy Limited
for their invaluable co-operation and suggestions.
VIII. R EFERENCES
[1] (2004) Kalki communicataion technologies. [Online]. Available:
http://www.kalkitech.com/downindex/IntroductionToABT.pdf
[2] G. Gross and F. D. Galiana, “Short-term load term forecasting,” Proceeding of IEEE, pp. 1558 – 1570, Dec. 1987.
[3] S. Rahman and R. Bhatnagar, “An expert system based algorithm for
short term load forecast,” IEEE Trans. Power Syst., pp. 392 – 398, 1988.
[4] K. L. Ho, “Short term load forecasting of Taiwan Power System using
a knowledge-based expert system,” IEEE Trans. Power Syst., pp. 1214 –
1221, 1990.
IX. B IOGRAPHIES
M. S. S. Rao received the M.Tech degree in Energy Systems Engineering,
from Indian Institute of Technology, Bombay, India, in 2005. Currently he is
pursuing Ph.D at IITB, Mumbai.
S. A. Soman is an Associate Professor in Department of Electrical Engineering, IITB, Mumbai, India. His research areas include Power System
Computation, Power System Protection, and Object Oriented Programming.
He has authored a book titled “Computational Methods for Large Power
System Analysis: An Object Oriented Approach”, published by Kluwer
Academic in 2001.
B. L. Menezes is an Associate Professor in KReSIT at the Indian Institute
of Technology, Bombay, India. His research areas include Forecasting, Data
Mining, and Network Security.
Pradeep Chawande received the M. Tech from Indian Institute of Bombay,
Mumbai, India in 1998, working as a Senior Manager in Reliance Energy
Limited. His research interests include Power System Protection, Numerical
Relays, Distribution Automation, and SCADA.
P. Dipti working as a Senior Engineer in Reliance Energy Limited, Mumbai.
Thu
40
Fri
22
Sat
5
T. Ghansyam working as a Senior Engineer in Reliance Energy Limited,
Mumbai.
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